globals [ max-consumers ]  ; don't let sheep population grow too large
; Sheep and wolves are both breeds of turtle.
breed [ consumers consumer ]  ; sheep is its own plural, so we use "a-sheep" as the singular.
breed [ businessmen businessman ]
turtles-own [ money ]       ; both wolves and sheep have energy
patches-own [ countdown ]

to setup
  clear-all
  ifelse netlogo-web? [set max-consumers 10000] [set max-consumers 30000]

  ; Check model-version switch
  ; if we're not modeling product, then the sheep don't need to eat to survive
  ; otherwise the product's state of growth and growing logic need to be set up
  ifelse model-version = "sheep-wolves-product" [
    ask patches [
      set pcolor one-of [ green brown ]
      ifelse pcolor = green
        [ set countdown product-regrowth-time ]
      [ set countdown random product-regrowth-time ] ; initialize product regrowth clocks randomly for brown patches
    ]
  ]
  [
    ask patches [ set pcolor green ]
  ]

  create-consumers initial-number-consumers  ; create the sheep, then initialize their variables
  [
    set shape  "cart"
    set color white
    set size 2  ; easier to see
    set label-color blue - 2
    set money random (2 * consumer-gain-from-food)
    setxy random-xcor random-ycor
  ]

  create-businessmen initial-number-businessmen  ; create the wolves, then initialize their variables
  [
    set shape "person business"
    set color black
    set size 2  ; easier to see
    set money random (2 * businessman-gain-from-food)
    setxy random-xcor random-ycor
  ]
  display-labels
  reset-ticks
end

to go
  ; stop the simulation of no wolves or sheep
  if not any? turtles [ stop ]
  ; stop the model if there are no wolves and the number of sheep gets very large
  if not any? businessmen and count consumers > max-consumers [ user-message "The sheep have inherited the earth" stop ]
  ask consumers [
    move
    if model-version = "sheep-wolves-product" [ ; in this version, sheep eat product, product grows and it costs sheep energy to move
      set money money - 1  ; deduct energy for sheep only if running sheep-wolf-product model version
      eat-product  ; sheep eat product only if running sheep-wolf-product model version
      death ; sheep die from starvation only if running sheep-wolf-product model version
    ]
    reproduce-sheep  ; sheep reproduce at random rate governed by slider
  ]
  ask businessmen [
    move
    set money money - 1  ; wolves lose energy as they move
    eat-consumer ; wolves eat a sheep on their patch
    death ; wolves die if our of energy
    reproduce-wolves ; wolves reproduce at random rate governed by slider
  ]
  if model-version = "sheep-wolves-product" [ ask patches [ grow-product ] ]
  ; set product count patches with [pcolor = green]
  tick
  display-labels
end

to move  ; turtle procedure
  rt random 50
  lt random 50
  fd 1
end

to eat-product  ; sheep procedure
  ; sheep eat product, turn the patch brown
  if pcolor = green [
    set pcolor brown
    set money money + consumer-gain-from-food  ; sheep gain energy by eating
  ]
end

to reproduce-sheep  ; sheep procedure
  if random-float 100 < consumer-reproduce [  ; throw "dice" to see if you will reproduce
    set money (money / 2)                ; divide energy between parent and offspring
    hatch 1 [ rt random-float 360 fd 1 ]   ; hatch an offspring and move it forward 1 step
  ]
end

to reproduce-wolves  ; wolf procedure
  if random-float 100 < businessmen-reproduce [  ; throw "dice" to see if you will reproduce
    set money (money / 2)               ; divide energy between parent and offspring
    hatch 1 [ rt random-float 360 fd 1 ]  ; hatch an offspring and move it forward 1 step
  ]
end

to eat-consumer  ; wolf procedure
  let prey one-of consumers-here                    ; grab a random sheep
  if prey != nobody  [                          ; did we get one?  if so,
    ask prey [ die ]                            ; kill it, and...
    set money money + businessman-gain-from-food     ; get energy from eating
  ]
end

to death  ; turtle procedure (i.e. both wolf nd sheep procedure)
  ; when energy dips below zero, die
  if money < 0 [ die ]
end

to grow-product  ; patch procedure
  ; countdown on brown patches: if reach 0, grow some product
  if pcolor = brown [
    ifelse countdown <= 0
      [ set pcolor green
        set countdown product-regrowth-time ]
      [ set countdown countdown - 1 ]
  ]
end

to-report product
  ifelse model-version = "sheep-wolves-product" [
    report patches with [pcolor = green]
  ]
  [ report 0 ]
end


to display-labels
  ask turtles [ set label "" ]
  if show-money? [
    ask businessmen [ set label round money ]
    if model-version = "sheep-wolves-product" [ ask consumers [ set label round money ] ]
  ]
end


; Copyright 1997 Uri Wilensky.
; See Info tab for full copyright and license.
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@#$#@#$#@
## WHAT IS IT?

This model explores the stability of predator-prey ecosystems. Such a system is called unstable if it tends to result in extinction for one or more species involved.  In contrast, a system is stable if it tends to maintain itself over time, despite fluctuations in population sizes.

## HOW IT WORKS

There are two main variations to this model.

In the first variation, the "sheep-wolves" version, wolves and sheep wander randomly around the landscape, while the wolves look for sheep to prey on. Each step costs the wolves energy, and they must eat sheep in order to replenish their energy - when they run out of energy they die. To allow the population to continue, each wolf or sheep has a fixed probability of reproducing at each time step. In this variation, we model the grass as "infinite" so that sheep always have enough to eat, and we don't explicitly model the eating or growing of grass. As such, sheep don't either gain or lose energy by eating or moving. This variation produces interesting population dynamics, but is ultimately unstable. This variation of the model is particularly well-suited to interacting species in a rich nutrient environment, such as two strains of bacteria in a petri dish (Gause, 1934).

The second variation, the "sheep-wolves-grass" version explictly models grass (green) in addition to wolves and sheep. The behavior of the wolves is identical to the first variation, however this time the sheep must eat grass in order to maintain their energy - when they run out of energy they die. Once grass is eaten it will only regrow after a fixed amount of time. This variation is more complex than the first, but it is generally stable. It is a closer match to the classic Lotka Volterra population oscillation models. The classic LV models though assume the populations can take on real values, but in small populations these models underestimate extinctions and agent-based models such as the ones here, provide more realistic results. (See Wilensky & Rand, 2015; chapter 4).

The construction of this model is described in two papers by Wilensky & Reisman (1998; 2006) referenced below.

## HOW TO USE IT

1. Set the model-version chooser to "sheep-wolves-grass" to include grass eating and growth in the model, or to "sheep-wolves" to only include wolves (black) and sheep (white).
2. Adjust the slider parameters (see below), or use the default settings.
3. Press the SETUP button.
4. Press the GO button to begin the simulation.
5. Look at the monitors to see the current population sizes
6. Look at the POPULATIONS plot to watch the populations fluctuate over time

Parameters:
MODEL-VERSION: Whether we model sheep wolves and grass or just sheep and wolves
INITIAL-NUMBER-SHEEP: The initial size of sheep population
INITIAL-NUMBER-WOLVES: The initial size of wolf population
SHEEP-GAIN-FROM-FOOD: The amount of energy sheep get for every grass patch eaten (Note this is not used in the sheep-wolves model version)
WOLF-GAIN-FROM-FOOD: The amount of energy wolves get for every sheep eaten
SHEEP-REPRODUCE: The probability of a sheep reproducing at each time step
WOLF-REPRODUCE: The probability of a wolf reproducing at each time step
GRASS-REGROWTH-TIME: How long it takes for grass to regrow once it is eaten (Note this is not used in the sheep-wolves model version)
SHOW-ENERGY?: Whether or not to show the energy of each animal as a number

Notes:
- one unit of energy is deducted for every step a wolf takes
- when running the sheep-wolves-grass model version, one unit of energy is deducted for every step a sheep takes

There are three monitors to show the populations of the wolves, sheep and grass and a populations plot to display the population values over time.

If there are no wolves left and too many sheep, the model run stops.

## THINGS TO NOTICE

When running the sheep-wolves model variation, watch as the sheep and wolf populations fluctuate. Notice that increases and decreases in the sizes of each population are related. In what way are they related? What eventually happens?

In the sheep-wolves-grass model variation, notice the green line added to the population plot representing fluctuations in the amount of grass. How do the sizes of the three populations appear to relate now? What is the explanation for this?

Why do you suppose that some variations of the model might be stable while others are not?

## THINGS TO TRY

Try adjusting the parameters under various settings. How sensitive is the stability of the model to the particular parameters?

Can you find any parameters that generate a stable ecosystem in the sheep-wolves model variation?

Try running the sheep-wolves-grass model variation, but setting INITIAL-NUMBER-WOLVES to 0. This gives a stable ecosystem with only sheep and grass. Why might this be stable while the variation with only sheep and wolves is not?

Notice that under stable settings, the populations tend to fluctuate at a predictable pace. Can you find any parameters that will speed this up or slow it down?

## EXTENDING THE MODEL

There are a number ways to alter the model so that it will be stable with only wolves and sheep (no grass). Some will require new elements to be coded in or existing behaviors to be changed. Can you develop such a version?

Try changing the reproduction rules -- for example, what would happen if reproduction depended on energy rather than being determined by a fixed probability?

Can you modify the model so the sheep will flock?

Can you modify the model so that wolves actively chase sheep?

## NETLOGO FEATURES

Note the use of breeds to model two different kinds of "turtles": wolves and sheep. Note the use of patches to model grass.

Note use of the ONE-OF agentset reporter to select a random sheep to be eaten by a wolf.

## RELATED MODELS

Look at Rabbits Grass Weeds for another model of interacting populations with different rules.

## CREDITS AND REFERENCES

Wilensky, U. & Reisman, K. (1998). Connected Science: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. International Journal of Complex Systems, M. 234, pp. 1 - 12. (The Wolf-Sheep-Predation model is a slightly extended version of the model described in the paper.)

Wilensky, U. & Reisman, K. (2006). Thinking like a Wolf, a Sheep or a Firefly: Learning Biology through Constructing and Testing Computational Theories -- an Embodied Modeling Approach. Cognition & Instruction, 24(2), pp. 171-209. http://ccl.northwestern.edu/papers/wolfsheep.pdf .

Wilensky, U., & Rand, W. (2015). An introduction to agent-based modeling: Modeling natural, social and engineered complex systems with NetLogo. Cambridge, MA: MIT Press.

Lotka, A. J. (1925). Elements of physical biology. New York: Dover.

Volterra, V. (1926, October 16). Fluctuations in the abundance of a species considered mathematically. Nature, 118, 558–560.

Gause, G. F. (1934). The struggle for existence. Baltimore: Williams & Wilkins.

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

* Wilensky, U. (1997).  NetLogo Wolf Sheep Predation model.  http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation.  Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 1997 Uri Wilensky.

![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png)

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.  To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This model was created as part of the project: CONNECTED MATHEMATICS: MAKING SENSE OF COMPLEX PHENOMENA THROUGH BUILDING OBJECT-BASED PARALLEL MODELS (OBPML).  The project gratefully acknowledges the support of the National Science Foundation (Applications of Advanced Technologies Program) -- grant numbers RED #9552950 and REC #9632612.

This model was converted to NetLogo as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227. Converted from StarLogoT to NetLogo, 2000.

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Line -7500403 true 15 150 285 150
Circle -7500403 true true 120 120 60
Line -7500403 true 216 40 79 269
Line -7500403 true 40 84 269 221
Line -7500403 true 40 216 269 79
Line -7500403 true 84 40 221 269

wolf
false
0
Polygon -16777216 true false 253 133 245 131 245 133
Polygon -7500403 true true 2 194 13 197 30 191 38 193 38 205 20 226 20 257 27 265 38 266 40 260 31 253 31 230 60 206 68 198 75 209 66 228 65 243 82 261 84 268 100 267 103 261 77 239 79 231 100 207 98 196 119 201 143 202 160 195 166 210 172 213 173 238 167 251 160 248 154 265 169 264 178 247 186 240 198 260 200 271 217 271 219 262 207 258 195 230 192 198 210 184 227 164 242 144 259 145 284 151 277 141 293 140 299 134 297 127 273 119 270 105
Polygon -7500403 true true -1 195 14 180 36 166 40 153 53 140 82 131 134 133 159 126 188 115 227 108 236 102 238 98 268 86 269 92 281 87 269 103 269 113

x
false
0
Polygon -7500403 true true 270 75 225 30 30 225 75 270
Polygon -7500403 true true 30 75 75 30 270 225 225 270
@#$#@#$#@
NetLogo 6.0.2
@#$#@#$#@
set model-version "sheep-wolves-grass"
set show-energy? false
setup
repeat 75 [ go ]
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
default
0.0
-0.2 0 0.0 1.0
0.0 1 1.0 0.0
0.2 0 0.0 1.0
link direction
true
0
Line -7500403 true 150 150 90 180
Line -7500403 true 150 150 210 180
@#$#@#$#@
1
@#$#@#$#@